Countries such as Pakistan, Afghanistan, Bangladesh and Sri Lanka have petitioned the U.S. for Covid-19 vaccines as the Biden administration prepares to share 80 million doses, which foreign governments say they need to slow the spread of the coronavirus.

Dozens of countries have sought a chunk of the doses the U.S. plans to donate overseas by the end of June, a senior administration official said.

“What the U.S. has is a gold mine,” Ravinatha Aryasinha, Sri Lanka’s ambassador to the U.S., said in an interview.

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The administration said it planned to share 60 million doses of the AstraZeneca PLC vaccine, following a safety review by the Food and Drug Administration, and 20 million doses from the vaccines from Moderna Inc., Pfizer Inc. and Johnson & Johnson, whose shots are being given to people in the U.S.

The Biden administration has faced growing pressure to share vaccine doses with developing countries amid outbreaks in India and Brazil. Mr. Biden said the U.S. would be a world leader in global vaccination efforts and characterized the 80 million doses as a first step.

Those doses represent a fraction of those needed to vaccinate much of the world’s eight billion population. Countries are desperate for any doses because of outbreaks and emerging variants, and there is limited supply as manufacturers increase production and expand capacity.

The Biden administration has said U.S. doses will be shared both directly with other countries and through Covax, a global initiative to deliver vaccines to developing countries. White House press secretary Jen Psaki told reporters last week that an announcement would be made soon on where doses would be distributed.

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A White House official said the National Security Council, Department of Health and Human Services, State Department and the U.S. Agency for International Development have been involved in determining where to send the doses. The administration has also been consulting people involved with Covax, vaccine manufacturers and others on considerations that include shipping doses out of the country, transporting them to different places and legal requirements, the person said.

Some vaccines require special cold-chain logistics, which could be difficult in some low-income countries.

The U.S. has fully vaccinated more than 50% of its adult population. But the administration has waited to share doses in part because it is trying to reach hesitant Americans and has begun vaccinating adolescents.

Last month, the administration said it supported a proposal from India, South Africa and other countries to share intellectual property of Covid-19 vaccines to help spur production. The drug industry and trade experts have said that such a move wouldn’t increase doses in the short term.

The world’s poorest 50 countries account for just 2% of the Covid-19 vaccines administered globally so far, according to the International Federation of Red Cross and Red Crescent Societies.

Bangladesh Foreign Minister A.K. Abdul Momen asked the U.S. in a May 7 letter to Secretary of State Antony Blinken for at least two million AstraZeneca doses immediately and another 10 million to 20 million later on.

Bangladesh made the request because it needs to administer second doses to about 1.6 million people and is willing to buy the doses if they can’t be donated, Mr. Momen said in an interview. He said he has made the request in meetings with U.S. officials here and in Bangladesh.

“We are in desperate need for this two million,” he said. “This has become a crisis.”

He said U.S. officials have said they are weighing the request.

A health worker preparing to administer a dose of Covid-19 vaccine last month in Dhaka, Bangladesh.

A health worker preparing to administer a dose of Covid-19 vaccine last month in Dhaka, Bangladesh.

Photo: Mortuza Rashed/Zuma Press

Bangladesh, with about 165 million people, has received seven million of the 30 million AstraZeneca doses it agreed to purchase from the Serum Institute of India, according to the letter. The letter also said India separately donated about 3.2 million doses to the country. Bangladesh also has agreements for China’s Sinopharm vaccine and Russia’s Sputnik V, according to Duke University’s Global Health Innovation Center, which tracks vaccine purchases.

In a letter to Mr. Biden on Sunday, Vietnamese President Nguyen Xuan Phuc asked for access to the 80 million doses and requested a phone call to discuss how their governments can cooperate on vaccine research and production.

Mr. Phuc wrote that although Vietnam has received doses through Covax, the country’s vaccination rate is low because global vaccine resources are hard to access.

After Mr. Biden announced plans to export AstraZeneca doses, Sri Lanka asked the U.S. to provide 600,000 doses so the country could give second shots to people in the country, Mr. Aryasinha said. He said the country has a shortfall because it stopped receiving doses from the Serum Institute of India after India banned exports.

More than 7% of the country’s more than 21 million people have received at least one dose, according to Our World in Data, a project based at Oxford University. The country has procured 28 million doses of various types, according to Unicef.

The country on May 18 asked for any Johnson & Johnson doses the U.S. can spare, Mr. Aryasinha said. He said the U.S. said officials are considering the requests, but the AstraZeneca doses couldn’t be provided at least until the FDA signs off on sharing the vaccine.

“If that gets cleared, our prayers would be answered,” Mr. Aryasinha said. Sri Lanka made its requests in letters to the administration and in meetings with U.S. officials.

Afghanistan asked the U.S. to provide doses directly to the country and through multilateral efforts such as Covax, according to a spokeswoman for the country’s embassy. Covax has allocated more than 2.5 million vaccine doses for Afghanistan and has given 468,000 doses of the AstraZeneca vaccine, the spokeswoman said. China has committed to providing 400,000 doses of Sinopharm’s vaccine, and India provided 500,000 doses of AstraZeneca PLC’s vaccine, she said.

Earlier this year, the U.S. said it would send a total of four million AstraZeneca doses, which officials described as a loan, to Mexico and Canada. Mr. Biden also announced an initial $2 billion investment in Covax in February and plans to release another $2 billion when other countries meet their commitments.

Write to Jared S. Hopkins at jared.hopkins@wsj.com and Sabrina Siddiqui at Sabrina.Siddiqui@wsj.com